Summing up, our results confirm both ancestry and temporal complexity shaping the still on-going process of genetic structuring of South Asian populations. This intricacy cannot be readily explained by the putative recent influx of Indo-Aryans alone but suggests multiple gene flows to the South Asian gene pool, both from the west and east, over a much longer time span.

Dienekes: "I haven't read the paper fully yet (it's open access), but the abstract seems to agree with what I've written both here and over at the Dodecad blog, about South Asians being primarily a West Asian/South Asian variable mix." In fact, the authors note in the body of the paper:

Another example of an heuristic interpretation appears when we look at the two blue ancestry components (Figure 2B) that explain most of the genetic diversity observed in West Eurasian populations (at K = 8), we see that only the k4 dark blue component is present in India and northern Pakistani populations, whereas, in contrast, the k3 light blue component dominates in southern Pakistan and Iran. This patterning suggests additional complexity of gene flow between geographically adjacent populations because it would be difficult to explain the western ancestry component in Indian populations by simple and recent admixture from the Middle East.

Moreover:

Both PC2 and k5 light green at K = 8 extend from South Asia to Central Asia and the Caucasus (but not into eastern Europe). In an attempt to explore diversity gradients within this signal, we investigated the haplotypic diversity associated with the ancestry components revealed by ADMIXTURE. Our simulations show that one can detect differences in haplotype diversity for a migration event that occurred 500 generations ago, but chances to distinguish signals for older events will apparently decrease with increasing age because of recombination. In terms of human population history, our oldest simulated migration event occurred roughly 12,500 years ago and predates or coincides with the initial Neolithic expansion in the Near East. Knowing whether signals associated with the initial peopling of Eurasia fall within our detection limits requires additional extensive simulations, but our current results indicate that the often debated episode of South Asian prehistory, the putative Indo-Aryan migration 3,500 years ago (see e.g., Abdulla15) falls well within the limits of our haplotype-based approach. We found no regional diversity differences associated with k5 at K = 8. Thus, regardless of where this component was from (the Caucasus, Near East, Indus Valley, or Central Asia), its spread to other regions must have occurred well before our detection limits at 12,500 years. Accordingly, the introduction of k5 to South Asia cannot be explained by recent gene flow, such as the hypothetical Indo-Aryan migration.

First, note that the k5 "light green" ADMIXTURE component does in fact extend into and throughout Europe (apart from Sardinia). The authors believe they've shown "k5" must have "spread" well before the Neolithic. What they've actually demonstrated is that ADMIXTURE (at least as used here) will not be the tool to disentangle complex recent population movements in Eurasia.